Your fund’s average return is lying to you

Investors often use the average return to gauge the performance of stocks, mutual funds, or portfolios. However, an average return may not accurately reflect the growth rate of money, as demonstrated by the difference between Fund A and Fund B. Both funds had the same arithmetic average return of 5%, but Fund A yielded Rs.1,10,500 while Fund B grew to Rs.1,21,551 over four years.

The discrepancy arises because losses have a greater impact on wealth than equivalent gains. For instance, a 20% drop reduces the principal to 80% of its original value. To recover, the investment must increase by 25%. This disparity, known as volatility drag, can lead to less wealth than anticipated based on the arithmetic average.

To account for compounding, investors can use the geometric average. This method multiplies 1 plus each periodic return, then takes the n-th root, where n is the number of periods. For Fund A, the geometric average is 2.53%, indicating that despite the 5% arithmetic average, the actual compounded annual growth rate is lower.

While the geometric average offers a better understanding of how returns compound, it doesn't provide insight into the investment's volatility. The compound annual growth rate (CAGR) addresses this by calculating the annualised growth rate between the starting and ending values. For Fund A, CAGR is also 2.53%, matching the geometric average.

However, CAGR doesn't reveal how the investment fluctuated during the period. Two investments can share the same CAGR but experience different levels of risk along the way. Investors should use arithmetic average, geometric average, and weighted average to avoid confusion among these distinct measures and make informed decisions.